Nuprl Lemma : reducible_wf
∀[a:ℤ]. (reducible(a) ∈ ℙ)
Proof
Definitions occuring in Statement :
reducible: reducible(a),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
reducible: reducible(a),
so_lambda: λ2x.t[x],
prop: ℙ,
and: P ∧ Q,
int_nzero: ℤ-o,
subtype_rel: A ⊆r B,
so_apply: x[s]
Lemmas referenced :
exists_wf,
int_nzero_wf,
not_wf,
assoced_wf,
equal-wf-base-T,
int_subtype_base
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
lambdaEquality,
productEquality,
setElimination,
rename,
hypothesisEquality,
natural_numberEquality,
intEquality,
applyEquality,
multiplyEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
Error :universeIsType
Latex:
\mforall{}[a:\mBbbZ{}]. (reducible(a) \mmember{} \mBbbP{})
Date html generated:
2019_06_20-PM-02_22_42
Last ObjectModification:
2018_09_26-PM-05_49_08
Theory : num_thy_1
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